I really need help with these 2 questions

Mathematics

1 answer:

igor_vitrenko [27]3 years ago

4 0

The question 6 is 2,150 meters question 7 is length 10w+64 meters
Width 25w+49 meters

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A survey was conducted that asked 1003 1003 people how many books they had read in the past year. results indicated that x overb

kirill115 [55]

The confidence interval is

$10.5\pm1.35 = (9.15, 11.85)$ . This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.

To find the confidence interval, we first find the z-score associated with it:

Convert 99% to a decimal: 0.99
Subtract from 1: 1-0.99=0.01
Divide by 2: 0.01/2 = 0.005
Subtract from 1: 1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58. Since both are equally far from this value we will use 2.575.

We calculate the margin of error using

$ME=z*\frac{s}{\sqrt{n}}
\\
\\=2.575*\frac{16.6}{\sqrt{1003}}=1.35$

This means that the confidence interval is
$10.5\pm1.35$

The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85

5 0

3 years ago

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$